Lecture 1 Pharmaceutical calculations

Pharmaceutics I

Lecture 1 Pharmaceutical calculations

Dr. Heidi M. Abdel Mageed, PhD Pharmaceutical Technology Dept

Future University in Egypt (FUE)

[email protected]

PHT 213

1 Dr. Heidi abdel Mageed

Dr. Heidi abdel Mageed 2

Course Instructors: Prof. Dalia Samuel Dr. Heidi A. Mageed

Credit Hours: 4 Lecture: 3 hrs/week Practical: 2 hrs/ week

Office Hours: Wednesday :1-2pm Thursday: 3-4 pm

Course Goals & Objectives

• Understand and practice pharmaceutical calculations for 2nd year pharmacy students

• To learn about pharmaceutical liquid preparations • Understand the development of liquid dosage forms

• Define Physico-chemical properties of pharmaceutical dosage forms and products and related concepts.

• Understand disperse systems in pharmaceutical preparations including suspensions , colloids and aerosols.


Lecture ILOs Metrology and Calculations:

• •Roman numbers

• •Measuring systems

• Dose conversions

• •Calculation of doses

• Calculations of child dose

• Alligation

• Objectives

• · Learn the commonly used subscription and signatura abbreviations.

• · Correctly interpret a prescription for compounding.

• Learn how to translate the signature

Learn how to label your prescription

Practice examples for pharmaceutical calculations will be available at the

copy center 4

Dr. Heidi abdel Mageed

Rx

Ammonium Chloride IV g

Liq. Extract of Liquorice Ӡ ml

Syrup 50 ml

Water q.s a.d C ml

Fiat: Cough syrup

Sig.: 5 ml t.i.d.

How to read ??


We can divide content of a

prescription into:

Drug +excipient= medicine

• Active ingredient= Drug

• Inactive ingredient

= excipients/additives

E.g. sweetening agent, coloring

agent…etc.

• vehicle

Solid,

liquids

and Vehicle

• Numericals

• Measuring

systems

Rx



Syrup 50 ml

Water q.s a.d C ml

Fiat: Cough syrup

Sig.: 5 ml t.i.d.


Roman numerals use a basic set of seven symbols:


1-When the second letter has a value smaller than

the first or equal the values are added .

ii = 2 Li =50+1=51

LXiv = 50+10+1-5= 64 lxxxviii = 88

2-When the second letter has a value greater than

the first , the smaller is to be subtracted.

Iv = 5-1=4 Xxiv = 24

xliv =44


3-I/X/C are used as subtractors

Each is used to be subtracted from the next 2 higher characters .

I V X L C D M e.g I is subtracted from v and x.

x is subtracted from l and C .

C is subtracted from D and M.

99=xcix

4-Any character cannot be repeated more than three times.

IIII does not exist


http://en.wikipedia.org/wiki/I

http://en.wikipedia.org/wiki/V

http://en.wikipedia.org/wiki/X

http://en.wikipedia.org/wiki/L

http://en.wikipedia.org/wiki/C

http://en.wikipedia.org/wiki/D

http://en.wikipedia.org/wiki/M

5-A subtractor is placed so as to proceed only

one character higher than itself.

e.g 19 is written xix not ixx.

6- Roman number is expressed as a method of

addition (only subtraction is done if there is

no other way).

e.g (8) is expressed as viii and not iix


An accurate way to write large numbers in Roman

numerals is to handle first

the thousands, then hundreds, then tens, then units.

Example: the number 1988.

One thousand is M

nine hundred is CM

eighty is LXXX

eight is VIII.

Put it together: (ⅯⅭⅯⅬⅩⅩⅩⅤⅠⅠⅠ)


The following mnemonics recall the order of Roman numeral values above ten, with L being 50,

C being 100,

D being 500,

and M being 1000.

Lucky Cows Drink Milk

Lucy Can't Drink Milk


Main difference between Arabic and

Roman numbers are that roman

numericals lack zero and the

numerical placement within a number

can sometimes indicate subtraction

rather than addition. Q???

Roman numerals remained in common use until about the 14th century, when they were replaced by Arabic numerals (thought to have been introduced to Europe from al-Andalus, by way of Arab traders and arithmetic treatises, around the 11th century).


http://en.wikipedia.org/wiki/Arabic_numerals



http://en.wikipedia.org/wiki/Al-Andalus



http://en.wikipedia.org/wiki/Arab

MEASUREMENT SYSTEMS

At least four different systems are currently

used in drug preparation and delivery:

☺the metric system

☺the apothecary system

☺the avoirdupois system

☺the household system


• The basic unit of weight in the metric system is the gram abbreviated

”g”

• The basic unit of volume in the metric system the liter, abbreviated “l”

• The basic linear unit of the metric system is

the meter, abbreviated “m”

The most commonly used units are:

Length: meter, centimeter, and millimeter.

Volume: liter, milliliter

Weight: gram, kilogram, milligram, and microgram.



PRACTICE PROBLEMS

• Add 7.25 L and 875 ml.

7.25 L = 7250 ml

Total = 7250 + 875 = 8125 ml

• A vitamin capsule contains 6.25 mcg of vitamin B12. How many capsules can be prepared from 1 g of vitamin B12?

1 g = 106 mcg

1 capsule 6.25 mcg

X capsule 106 mcg

X = 106 / 6.25 = 160,000 capsule


• Aspirin tablets contain 325 mg of aspirin. How many tablets can be prepared from 5 kg of aspirin?

5 kg = 5 x 106 mg

1 tablet 325 mg

X tablet 5 x 106 mg

X = 5 x 106 / 325 = 15384 tablet

• If an injectable solution contains 25 mcg of a drug in each 0.5 ml. how many milliliter will be required to provide a patient with 0.25 mg of the drug?

25 mcg = 0.025 mg

0.5 ml 0.025 mg

X ml 0.25 mg

X = 0.25 x 0.5 / 0.025 = 5 ml



Remember:

• Avoirdupois – used in measuring bulk medications (pounds, ounces, grains)

• Apothecary – developed after the Avoirdupois

system to enable fine weighing of medications (pounds, ounces, drams, scruples, grains,

gallons, pints, fluid ounces, fluid drams,

minims)

• Household – commonly used to measure liquids with home utensils (teaspoons,

tablespoons, cups)

It has two divisions of measurement:

weight and volume

The basic unit of weight is the grain,

abbreviated gr, and never capitalized;

the basic unit of volume is the

minim

An interesting feature of this system is

that it uses Roman numerals placed

after the unit of measure to denote

amount.

For example,

15 grains would be

written

“gr xv.”

This system is the one used in

the United States

for weight only and is use

d in commercial buying

and selling.

The basic unit of the avoir-

dupois system is also the

grain.

The name derives from a misspelling of the

Old French term aveir de peis meaning

literally "goods of weight", referring to

goods sold by weight

In the avoirdupois system, all units are

multiples or fractions of the pound.


http://en.wikipedia.org/wiki/Old_French




For Mass Measurment

Unit Symbol Division Grains SI units

Pound ℔ 12 ounces 5760 373.242 g

Ounce ℥ 8 drams 480 31.103 g

Drachm ʒ 3 scruples 60 3.888 g

Scruple ℈ 20 grains 20 1.296 g

Grain G 1 64.8 mg


http://en.wikipedia.org/wiki/SI

http://en.wikipedia.org/wiki/Pound_(weight)

http://en.wikipedia.org/wiki/Ounce

http://en.wikipedia.org/wiki/Dram_(unit)

http://en.wikipedia.org/wiki/%C6%B7

http://en.wikipedia.org/wiki/Scruple

http://en.wikipedia.org/wiki/Grain_(measure)

For Volume Measurements

Unit Symbol Division Minims SI units

Gallon

Quarts

gal.

qt.

4 quarts

2 pints

61440

15360

4.54609 L

Pint pt. 16 ounces 7680 568.26 mL

Ounce oz. 8 drachms 480 28.413 mL

Drachm dr.

60 minims

60 3.5516 mL

Minim min. 1 0.0592 mL 24 Dr. Heidi abdel Mageed

http://en.wikipedia.org/wiki/SI

http://en.wikipedia.org/wiki/Gallon

http://en.wikipedia.org/wiki/Pint

http://en.wikipedia.org/wiki/Ounce

http://en.wikipedia.org/wiki/Dram_(unit)

http://en.wikipedia.org/wiki/Minim

Ex: Reduce sum of ss oz/ Ʒii /Эi to grain ( Apothecaries measure of weight)

ss = ½ × 480 gr. = 240 gr.

Ʒii = 2 × 60 gr. =120 gr.

Эi = 1× 20 gr. = 20 gr.

380 gr.

convert iv and Ʒiiss to drachms. ( Apothecaries measure of volume)

f v = 5 × 8 f Ʒ = 32 f Ʒ

f Ʒiiss = 2 ½ f Ʒ

34½ f Ʒ

PRACTICE PROBLEMS


Relationship of Avoirdupois and Apothecaries, weight

The grain is the same in both the avoirdupois and apothecaries, systems

of weight but other denominations with the same names are not equal.

To convert from either system to the other, first reduce the given quantity

to grains in the one system, and then reduce the result to any desired

denomination in the other system


.

EX: Convert ii and Ʒii to OZ in avoirdupois weight. ( Apothecaries measure of weight)

ii = 2 × 480 gr. = 960 gr.

Ʒii = 2 × 60 gr. = 120 gr.

Total 1080 gr.

1 oz.= 437.5 gr.

1080 / 437.5 = 2 oz. 205 gr. ( Avoirdupois measure of weight)

EX: How many grains of a drug are left in a 1 ounce (avoirdupois) bottle after enough amount

of it has been used to make 2000 tablets each containing 0.1 gr of the drug?

1 ounce = 437.5 gr.

The used amount = 2000 x 0.1 = 200 gr.

The remaining amount = 437.5 – 200 = 237.5 gr.

Ex: If a drug costs $ 1.75 per oz. what is the cost of 2 Ʒ?

1 oz. = 437.5 gr., and 2 Ʒ × 60 = 120 gr.

437.5 gr. X 1.75 $

120 gr. ?

= $ 0.48




Conversions between metric and common systems

Some Practical Equivalents

Conversion of Liquid Quantities

a- to convert metric volumes to apothecaries fluid equivalents :

For small volumes, X No. of ml by 16.23 to get minims and reduce the result to measurable

units if necessary.

For larger volumes, reduce to ml and ÷ by 29.57 to get f or by 473 to get (

pt.)

Ex: Convert 0.4 ml to minims.

0.4 ml × 16.23 m = 6.492 or ~ 6.5 m

EX: Convert 2.5 L to fluidounces

2.5 L × 1000 = 2500 ml

1 f X 29.57 ml

? 2500 mlv

= 84.5 f


Conversion

b- to convert apothecaries fluid volumes to metric equivalents:

For small volumes , reduce to minims and ÷ by 16.23 to get ml.

For large volumes, reduce to f and X by 29.57 to get ml.

Ex: Convert f Ʒ iiss to milliliters

F Ʒ iiss = 2 ½ × 60 m = 150 m

1 ml X 16.23 m

? ml 150 m

= 9.24 ml


Conversion of Weights

a- To convert metric weight to common weights: ( apothecaries & avoirdupois systems)

For small quantities reduce to gm and X by 15.432 or ÷ by 0.065 to get grains , and reduce the

quantity to any desired denomination.

For larger quantities reduce to gm and ÷ by 31.1 to get apothecaries ounces , or ÷ by 28.35 to

get avoirdupois ounces or ÷ by 454 to get pounds avoirdupois.

EX: Convert 12.5 gm to grains.

12.5 × 15.432 gr. = 192 gr. Or

12.5 ÷ 0.065gr. = 192 gr.

EX: Convert 5 gm to grains

1 g. X 15.43 gr

5 g. ---gr = 77 gr.

EX: Convert 15 kg. to pounds avoirdupois

1 kg X 2.2 Ib

15 kg ? Ib

= 33.0 Ib



These combine bits of both the apothecary and avoirdupois systems and also

throws in a couple of measures found in neither system

This system uses the teaspoon

as the basic unit of fluid measure

and the pound as the basic unit of solid measure.




Rx


Liq. Extract of Liquorice fӠ ml

Syrup 50 ml

Water q.s a.d C ml

Fiat: Cough syrup

Sig.: 5 ml t.i.d.


A label of a suitable size should be placed on the container, this label should be placed for two reasons:

1) To identify the contents of the container .

2) To ensure that the patient have concise information which will enable him to use his medication in the most effective and appropriate way.


The name of the preparation on the label

comes from Fiat in the prescription.

The name should be centered.

The instruction to the patient on the label

comes from Sig. in the prescription.

Leave an indent before writing the

instruction.


Read this prescription

Rx



Syrup 50 ml

Water q.s a.d 100 ml

Fiat: Cough syrup

Sig.: 5 ml t.i.d.


• Sig. Write on Label

• Aq. Water

• b.i.d Twice a day

• t.i.d Three times daily

• m.d.u To be used as directed

• t.d.u To be taken as directed

• n.m Night and morning

• o.n Every night

• o.m Every morning

• q.i.d. Four times a day

• a.c Before meals

• p.c After meals

• h.s At bedtime


The Cough Syrup

One teaspoonful to be taken

three times daily.


• If no instructions are written and the

medication is for internal use , then

• Write →To be taken as directed.

• If the medication is for external use, then

write → To be used as directed.

– White label is used for internal preparation.

– Red label is used for external preparation.


Units of Measure cont.

(Equivalencies) • Equivalencies among systems

– 1 inch = 2.54 cm

– 1 kg = 2.2 pounds (lb)

– 1 fluid ounce (fl oz) = 29.57(30) milliliters (ml)

– 1 pint (pt) = 473.167 (480) milliliters (ml)

– 1 teaspoonful (tsp) = 5 milliliters (ml)

– 1 tablespoonful (TBS) = 15 milliliters (ml)

– 1 ounce (oz) = 28.35 grams (g)

– 1 pound (lb) = 453.59 (454) grams (g)

• Fill in the blanks:

a.1 liter (L) = ________ml

b.1000 g = __________kg

c.1 g = _____________mg

d.1000 mcg =_________mg

e.1 tbsp = ____________tsp

f. 1 tsp =_____________ml

g. 2 fl oz =_____________ml

h.70 kg = ______________pounds (lb)

Don’t

memorize

this table!


Office hours:

Wednesday 10-11 am

Thursday 1-2 pm


Documents

Lecture 1 Pharmaceutical calculations